WASHINGTON—President Obama said Tuesday that the administration is investigating how counterterrorism authorities handled intelligence about Tamerlan Tsarnaev and his mother to determine if American can do a better job of preventing future terrorist attacks by self-radicalized individuals.

``When an event like this happens, we want to review every step that was taken, we want to leave no stone unturned, we want to see if there is in fact additional protocols and procedures that could be put in place that would further improve and enhance our ability to detect a potential attack,’’ Obama said in a White House press conference.

He was reacting to a reporter’s question about a Globe report Monday night that Obama’s director of national intelligence, James R. Clapper, has ordered the review, which will be conducted by the Intelligence Community Inspector General.

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``Part of what Director Clapper is doing is to see if we can determine lessons learned from what happened’’ in Boston on April 15, Obama said.

Two bombs exploded near the Boston Marathon finish line, killing three people and injuring more than 260. Tamerlan Tsarnaev died after a confrontation with police on April 19. His younger brother, Dzhokhar, also a suspect in the bombings, was captured in Watertown on the evening of April 19 and remains in custody.

Obama defended the work of the FBI, Department of Homeland Security, and state and local police in Massachusetts in quickly taking steps that led to the killing and capture of the alleged suspects. The president said criticism from South Carolina Senator Lindsey Graham, who has said the FBI and other authorities apparently dropped the ball by not more closely scrutinizing the older Tsarnaev, is ``not right, although I am sure it generated some headlines.’’

``It’s not as if the FBI did nothing,’’ Obama said. ``They not only investigated the older brother, they interviewed the older brother, they concluded that there were no signs he was engaging in extremist activity.

``The question then is, is there something that happened that triggered radicalization and an actual decision by the older brother to engage in the tragic attack we actually saw in boston, and are there additional things that could have been done in the interim that might have prevented it?’’

He said Russia has been cooperative in providing information about Tsarnaev’s travels to Russia in 2012 and its warnings in 2011 to the FBI and the CIA about his increasing radicalization. But he alluded to decades of distrust between the countries.

``Obviously old habits die hard,’’ he said. ``There there are still suspicions between our intelligence and law enforcement agencies that date back 10, 20, 30 years, back to the Cold War.’’

The trouble, he said, is identifying lone actors who are not part of broader terror networks.

``One of the dangers we now face are self-radicalized individuals, who are are already here in the United States and in some cases may not be in any kind of network, but because of whatever warped and twisted ideas they may have decide to carry out an attack,’’ Obama said.

``Those,’’ he said, ``in some ways more difficult to prevent’’ than attacks engineered by Al Qaeda operatives or other terrorists overseas.

Obama also lauded the response by Boston residents in the face of the shocking bombings at a cherished annual event.

``I think everybody can take a cue from Boston,’’ he said. ``You don’t get a sense that anyone is intimidated when they go to Fenway Park a couple of days after the bombing. And there are joggers right now, I guarantee you, all throughout Boston and Cambridge and Watertown. ...

``We’re not going to stop living our lives because of warped, twisted individuals trying to intimidate us.’’